1. Field of the Invention
The present invention-generally relates to the computation of trigonometric expressions, and more specifically to a method and apparatus for generating higher-order sine and cosine sequences. The invention is particularly useful in direct access storage devices (e.g., hard disk drives) of a computer system, for reducing the effects of local, repeatable position errors which can otherwise lead to track misregistration.
2. Description of Related Art
In modern manufacturing and design, there is a constant desire to reduce the size (and weight) of nearly every type of consumer product, including various electromechanical devices. As these devices become ever smaller, and more complicated, they place increasingly difficult demands on system designers to improve the precision and accuracy of any moving parts which require exact registration or positioning. One example of this trend may be found in direct access storage devices (DASDs) used by computer systems for permanent retention of data and application programs.
The most common type of DASD in use today is often referred to as a hard disk drive, or HDD. FIG. 1 depicts an exemplary HDD 10 constructed in accordance with the prior art. HDD 10 has a shroud or enclosure 12, a plurality of disks 14, a rotary actuator assembly 16, and associated control electronics (not shown). A cover which is part of enclosure 12 has been removed in FIG. 1. Disks 14 are appropriately mounted on a spindle 20 which is attached to a spindle motor, and thus rotatable with respect to enclosure 12.
The upper and lower surfaces of each of the disks 14 are coated with a magnetic material to allowing the writing of data onto the surfaces using the principle of magnetic induction. Rotary actuator assembly 16 has a plurality of arm/suspension members 18 supporting electromagnetic transducers (heads) at their tips, which are used to read data from and write data to the magnetic media-bearing surfaces of disks 14. The movement of actuator assembly 16 is controlled by a voice-coil motor (VCM) 22.
The magnetic media-bearing surfaces of disks 14 have a plurality of generally concentric tracks for recording blocks of information. Each of these tracks is divided into multiple sectors. The theoretical location of any given set of data bits can accordingly be computed based on the track number and position within the particular sector. Based on this assumed location, the HDD control electronics generate appropriate electrical signals that cause VCM 22 to move the read/write heads on arm/suspension members 18 over the desired portions of disks 14. Thus, when the heads have been located over the proper tracks, as the disks 14 are spinning, data can be read from or written to the tracks via the inductive heads.
Not surprisingly, the read/write heads on the arm/suspension assembly may not achieve a perfect registration with the desired tracks of the spinning disks. Many such position errors are repeatable, although they may vary from track-to-track. Spatial frequency analysis of the repeatable position error (RRO) from track-to-track reveals substantial differences in the harmonic signal content. Very low correlation between phase and amplitude of second and higher harmonic (xe2x80x9clocalxe2x80x9d) RROs for adjacent tracks have been observed. The first harmonic (xe2x80x9cglobalxe2x80x9d) RRO, which expresses a disk-slip, is usually well correlated between tracks on a given surface.
The large variations in RRO from track-to-track can often be attributed to characteristics which are fixed during the servo-track-write (STW) time. Factors that may contribute to local RRO include: arm and suspension resonances at STW; spindle bearing frequencies at STW; airflow and turbulence at STW; external vibrations at STW; media defects (low coercivity) that changes the integrity of the linearity and offset of the local servo-pattern transfer function; and spindle imbalance. The repeatable runout, frozen in at STW time, reflects arm/suspension and bearing resonances in the mechanical disk drive structure. When the actuator tries to follow the frozen-in track, the mechanical forces (vibrations) generated will be of frequencies that may re-excite the resonances in the structure. Servo writing at a lower RPM might reduce the re-excitement of some of the arm/suspension resonances, but this adds to I/O latencies.
The prior art uses various techniques to attempt to correct misregistrations of the read/write heads. For example, a position error signal (PES) may be generated as the head attempts to read track information, and this PES can be used to correct the head location. There are limits on the effectiveness of PES correction, however, particularly relating to the amount of time that is required to generate and process the PES to provide the corrective factor. As the physical size of DASDs shrinks, the foregoing problems are only exacerbated further. It would, therefore, be desirable to devise an improved method for high speed generation of track registration information. It would be further advantageous if the method could provide an in-situ, seal-healing approach to reduce the effects of local repeatable position errors on all tracks in a DASD. Such a method would benefit from improvements in calculating higher-order harmonics (i.e., sine and cosine sequences) that could implement local feedforward and PES-correction in a lowcost and efficient manner. Common algorithms, like the recursive Chebyshev polynomial algorithm, have been employed for generating such higher-order sequences, but such algorithms require a series of multiplications and are not suitable in fast, real-time applications with limited computational capabilities.
It is therefore one object of the present invention to provide an improved method of registering moving parts within an electromechanical device.
It is another object of the present invention to provide such a method which may be used to improve track registration in a direct access storage device.
It is yet another object of the present invention to provide a lowcost and efficient method of generating higher-order sine and cosine sequences that may be used for correcting registration of such moving parts.
The foregoing objects are achieved in a method of generating a higher-order trigonometric sequence, generally comprising the steps of constructing a table having a plurality of values arranged as a finite-length, first-order trigonometric sequence, indexing the table to yield a different sequence of the values, based on an order number of a desired higher-order harmonic, and catenating the values according to the different sequence to yield a higher-order trigonometric sequence whose order is the order number. The table may be a finite-length, first-order sine sequence, with the method yielding a higher-order sine sequence, or the table may be a finite-length, first-order cosine sequence, with the method yielding a higher-order cosine sequence. The table has a period N, and the indexing step computes a plurality of pointer indices equal to (k*n)mod(N), where k is the order number, and 0xe2x89xa6n less than N. In the special case where N is a multiple of 4, a single table may be used for both higher-order sine and higher-order cosine sequences.
The method of generating the higher-order trigonometric sequences may advantageously be applied to the calculation of a local PES-correction value for at least one track of a direct access storage device. The local PES-correction value is then used to position a read/write head of the direct access storage device over the track. In a preferred implementation, the PES-correction value for the track is stored on a sector of the direct access storage device.
The above as well as additional objectives, features, and advantages of the present invention will become apparent in the following detailed written description.